Why Can Modern Governments Tax So Much?

Working paper Why Can Modern Governments Tax So Much? An Agency Model of Firms as Fiscal Intermediaries Henrik Jacobsen Kleven Claus Thustrup Kreiner Emmanuel Saez March 2012 When citing this paper, please use the title and the following reference number: S-1004-NOC-1

Why Can Modern Governments Tax So Much? An Agency Model of Firms as Fiscal Intermediaries Henrik Jacobsen Kleven, London School of Economics and CEPR Claus Thustrup Kreiner, University of Copenhagen and CESifo Emmanuel Saez, UC Berkeley and NBER March 2012 Abstract This paper presents a simple agency model to explain why third-party income reporting by employers dramatically improves income tax enforcement. Modern firms have a large number of employees and carry out complex production tasks, which requires the use of accurate business records. Because such records are widely used within the firm, any single employee can denounce collusive tax cheating between employees and the employer by revealing the true records to the government. We show that, if a firm is large enough, such whistleblowing threats will make tax enforcement successful even with low penalties and low audit rates. Embedding this agency model into the standard Allingham-Sandmo tax evasion model, we show that third-party reporting improves tax enforcement if the government disallows self-reported losses or audits such losses more stringently, which fits with actual tax policy practices. We also embed the agency model into a simple macroeconomic growth model where the size of firms grows with exogenous technological progress. In early stages of development, firms are small, tax rates are severely constrained by enforcement, and the size of government is too small. As firm size increases, the enforcement constraint is slackened, and government size is growing. In late stages of development, firm size is sufficiently large to make third-party tax enforcement completely effective and government size is socially optimal. We would like to thank David Albouy, Tim Besley, Saki Bigio, Raj Chetty, Alain Jousten, Wojciech Kopczuk, Camille Landais, Thomas Piketty, Monica Singhal, Joel Slemrod, and numerous seminar participants for helpful discussions and comments. Corresponding author: Emmanuel Saez, University of California, Department of Economics, 549 Evans Hall #3880, Berkeley, CA 94720, email: saez@econ.berkeley.edu. This paper is an output of the International Growth Centre (IGC). Additionally, financial support from NSF Grant SES-0850631 is gratefully acknowledged.

1 Introduction The size of governments has expanded dramatically over the 20th century. A central element of this expansion has been the ability of governments to extract a substantial fraction of national products through taxation without destroying economic growth. In all advanced economies, most taxes are collected through third-party institutions such as private or public employers, banks, investment funds, and pension funds. These entities (which we call firms ) generally have a large number of employees, clients, or business partners. Therefore, they need to use accurate and rigorous records to carry out their complex business activities. Firms report taxable income such as corporate profits, compensation paid to employees, or capital income paid to clients directly to the government, and therefore act as a third party between households and the government. They also often withhold taxes on behalf of the government so that tax payments take place as-you-go. 1 It is widely known in the tax law literature (e.g., Surrey 1958; Lederman 2009) as well as among tax practitioners (e.g., Bird 2003; OECD 2004, 2006) that tax enforcement is excellent whenever such third-party reporting is in place, and that enforcement is weak even in the most advanced economies when such third-party reporting is not in place, as in the case of small family businesses. Therefore, as a first approximation, tax enforcement is successful if and only if third-party reporting covers a large fraction of taxable income. For example, the most recent US Tax Compliance Measurement Study (Internal Revenue Service, 2006) shows that individual income tax evasion rates is 53.9% when there is little or no information reporting, but that the evasion rate is less than 5% when there is substantial information reporting. 2 In spite of its central importance, the theoretical literature on tax evasion has not devoted much attention to the issue of third-party reporting or tried to explain why such a system is successful. Indeed, most of the modern literature on tax evasion follows on the seminal study by Allingham and Sandmo (1972), which used the Becker (1968) model of crime and focuses on a situation with no third-party reporting, i.e., on the case where enforcement is never successful 1 The withholding system is useful to individuals or companies when there are credit constraints, a point we will not investigate in this paper where we focus only on informational aspects. 2 Similarly, Kleven et al. (2009) study an income tax audit experiment in Denmark and find that, although purely self-reported income constitutes only about 8% of total reported income, it accounts for about 90% of detected evasion. Eurostat (2007) uses a questionnaire on undeclared work in the European Union and shows that it is concentrated primarily among the self-employed providing direct services to households. 1

in practice and which covers a minor part of taxation in advanced economies. 3 The Allingham- Sandmo model generates a key puzzle: why are compliance rates so high in developed countries given that audit rates and penalties for tax evasion are generally very low? 4 Our paper sets out a three-tiered agency model to provide a simple micro-foundation for the success of third-party reporting. In the model, the government is the top tier (principal) trying to extract tax revenue from individual income earners (bottom tier agents) who are employed or paid by firms (middle tier). The firm acts as a third party that reports income on behalf of individuals. Although we focus on the case where individuals are employees of the firm, the model can easily be applied to a situation where individuals are clients investing their savings and receiving capital income from a financial institution, or shareholders receiving profits from the firm. When a firm is large and complex, using detailed business records such as accounting books, details of purchases and sales, or payroll accounts listing individual wages and salaries is extremely valuable for productivity. Such records are widely used within the firm and hence many employees know about them. In principle, the firm and its employees could collude to report smaller incomes salaries and profits to the government than those actually earned. Under perfect information and commitment between the firm and individuals, there would be no reason for breaking the collusion. In practice, breakdowns can occur because of random shocks such as conflicts between employees and the employer, moral concerns of a newly hired employee, or an employee mistakenly showing the true business records to tax inspectors. Breakdowns can also occur as a result of rational whistleblowing if the government provides rewards to whistleblowers and firms cannot make employees commit not to whistleblow ex-ante. In our model, we assume that each employee has the option of reporting cheating to the government by divulging the true business records to the government. When a firm has many employees, breakdowns of collusion will occur with a high probability. Critically, it is the combination of a large number of informed employees and the existence of business records evidence, which makes third-party tax enforcement successful. 5 3 See Andreoni et al. (1998), Cowell (1990), Schneider and Enste (2000), Slemrod and Yitzhaki (2002), Slemrod (2007), and Shaw, Slemrod, and Whiting (2008) for comprehensive surveys. 4 As Andreoni et al. (1998) conclude at the end of their survey (p. 855): The most significant discrepancy that has been documented between the standard economic model of compliance and real-world compliance behavior is that the theoretical model greatly over-predicts noncompliance. Various studies suggest that high compliance rates may be explained by psychological or behavioral aspects such as social norms, tax morale, patriotism, guilt and shame (e.g., Cowell 1990, chapter 6; Andreoni et al. 1998, Section 8). In this paper, we propose instead a theory explaining high compliance based on information. 5 Our model focuses on internal information sharing within the firm. However, firms also share information 2

We embed this agency model into the Allingham and Sandmo (1972) model of tax evasion assuming that some income items (such as wages and salaries) are third-party reported, while other income items are solely self-reported (such as self-employment income). We first demonstrate a surprising third-party irrelevance result: even if the government can observe third-party reported items perfectly at no cost, third-party reporting will be entirely undone by individual tax filers who adjust self-reported income correspondingly. However, this irrelevance result depends critically on two assumptions: self-reported losses are allowed and audit rates are independent of the level (or sign) of self-reported income. In practice, self-reported income losses are often disallowed to count against other income items, and tax audits are concentrated on self-reported income and especially self-reported income losses. In those circumstances, the irrelevance result no longer holds and third-party reporting does reduce overall tax evasion. The last part of the paper embeds our agency model into a simple macroeconomic growth model where the size and complexity of firms grows with exogenous technological progress. In this model, a representative individual has preferences over private and public goods. In the absence of enforcement problems, taxes are non-distortionary and should be set to finance public goods according to the classical Samuelson rule. We model utility functions such that the public good has an income elasticity equal to one, implying that the first-best tax rate is constant along the path of economic growth. With tax enforcement constraints, however, there are three regimes over the process of development. In the earliest stage, firms are very small and untaxable, and therefore the government raises no tax revenue and supplies no public goods. In the middle stage, firm size is large enough that firms start becoming taxable provided that the tax rate is not too high. In that stage, the enforcement constraint is binding, and the government tax rate and public goods provision are below the first-best level but growing over time. In the latest stage, firms have become so large that, even under the first-best tax rate, firms choose to remain in the formal sector and pay taxes. The government imposes the first-best tax rate and government size relative to output is optimal and stable over time. 6 This simple macro model can account for the historical growth in government size over the with external parties such as other businesses and individual clients, shareholders, or debt holders. The number of such external parties also grows with economic development, making tax collusion more di cult as in our internal information sharing model. 6 Although we present the theory in the context of a benevolent government maximizing the welfare of a representative household, the story is consistent with a Leviathan view of government where self-interested politician-bureaucrats maximize tax revenue. 3

last century and the stability of government size since the 1970s in the richest economies. The theoretical story does not rely on demand for public goods e ects or political economy e ects. Our theory shows that technological progress and economic growth leads to large and complex firms, which can then be easily taxed. Therefore, our theory shows that capitalism in the sense of the emergence of large and complex firms using rigorous accounting is a necessary condition for the rise of large welfare state governments, which fund public programs such as welfare programs, social insurance programs, retirement benefits, and education. This can be seen as a Marxist theory in minor mode: rather than leading to revolution and communism, capitalism, by relaxing the tax enforcement constraint, breads large welfare states. The paper is organized as follows. Section 2 reviews the related literatures. Section 3 presents our micro-model of third-party tax enforcement and then embeds this model into a standard Allingham-Sandmo model of tax evasion. Section 4 embeds the micro-model in a simple macroeconomic framework which accounts for the evolution of government size over the course of development. Finally, Section 5 o ers concluding remarks. 2 Review of Related Literature 2.1 Literature on Tax Evasion and Tax Enforcement Our agency model of third-party tax enforcement contributes to the large literature on tax evasion and tax enforcement. A few previous studies have incorporated information reporting into tax evasion models. Yaniv (1992) made the simple but important point that, if the employer and employees can collude, then third-party reporting cannot help tax enforcement. Our paper starts from this benchmark and shows that this collusion equilibrium is fragile in the presence of verifiable business records and many employees. Recently, a number of studies have made important progress in modelling the problem of tax enforcement. First, Gordon and Li (2005) develop a model where the government can collect taxes only from formal firms defined as those connected to the financial sector. Access to credit is indeed one way in which using rigorous accounting books improves productivity. They show how the lessons from optimal tax theory are drastically changed in this environment and fit much better with actual tax policies. Instead of considering a reduced-form model of tax enforcement, our paper zooms in on the micro-foundations of third-party reporting by explicitly modelling the tax evasion game in a three-tiered agency model and is fully consistent with the 4

contribution of Gordon and Li (2005). Second, Kopczuk and Slemrod (2006) set out a simple model to show how the network of firm-to-firm arm-length transactions can help the government enforce taxation. In that context, the authors demonstrate formally the important point that value-added taxes and retail sales taxes are no longer equivalent as value added taxes are easier to enforce using firm-to-firm transaction information. Third, Keen (2007) shows that a valueadded-tax allows to tax informal suppliers because formal businesses cannot take a deduction for purchases from informal suppliers. Our paper focuses primarily on the within-firm information network rather than the across-firm information network and is therefore complementary to the Kopczuk-Slemrod and Keen papers. 7 Finally, a number of studies in the corporate income tax evasion literature have shown that the internal organization or the external activities of firms can a ect their tax reporting decisions. 8 At a broad level, our paper is related to the large theoretical literature on mechanism design and implementation, especially work on mechanism design in environments with complete information among agents (such as employees in a firm). This literature has been surveyed by Moore (1992), who showed that cross-reporting is a powerful instrument that often allows the principal to elicit truthful information from agents, at least in a non-cooperative setting and if large fines are feasible. Our model of third-party reporting encompasses this basic idea, although we allow for the possibility of collusive behavior and assume (realistically) that there is a upper bound on the size of fines, both of which makes tax enforcement harder. In this case, it is not always feasible to achieve truthful reporting and the e cacy of enforcement depends on firm size. We come back to these mechanism design issues below, where we discuss the potential for non-conventional tax enforcement mechanisms to improve the truthfulness of income reporting. 2.2 Literature on the Growth of Government Our macro model contributes to a very long literature trying to explain the growth of government. A number of theories have been put forward. First, the famous Wagner s law (after 7 We discuss briefly how the network of firm-to-firm transactions can also help enforcement as firms can also denounce tax cheating of other firms. 8 On the internal side, Crocker and Slemrod (2005) develop a shareholder-manager agency model with tax evasion showing that penalties imposed on managers are more e ective in reducing evasion than penalties imposed on shareholders. Chen and Chu (2005) show that the evasion decision of the firm s owner a ects the optimal compensation scheme o ered to employees and hence creates a distortion in the manager s e ort and reduces the e ciency of the contract. On the external side, Bayer and Cowell (2005) show that imperfect competition between firms have important consequences for the e ciency e ects of corporate tax audits. 5

the German economist Adolph Wagner, 1835-1917) focuses on the demand side and posits that public goods have an income elasticity above one (see Musgrave, 1966, for a detailed exposition and analysis). Second, Baumol s cost disease theory focuses on the supply side and posits that, over the course of development, productivity in the private sector increases while productivity in the public sector stagnates, leading to a growth of government spending relative to GDP (Baumol and Bowen, 1966; Baumol, 1967). Third, Peacock and Wiseman (1961) proposed a ratchet e ect theory, whereby temporary shocks such as wars raise government expenditures, which do not fall back after the shock as social norms regarding the proper level of public goods and taxation are permanently a ected by the temporary shock. Notice that the Wagner, Baumol, and ratchet e ect theories cannot explain the long period of stable government expenditures before the 20th century, a period with some economic growth and with many wars creating temporary spending shocks. Fourth, the Leviathan theory posits that governments are controlled by self-interested politician-bureaucrats, unchecked by electoral constraints (Brennan and Buchanan, 1980), and hence maximize revenue under constitutional and fiscal constraints. Although proponents of the Leviathan theory have focused primarily on public choice and constitutional aspects, this theory is entirely consistent with the importance of tax enforcement constraints that we emphasize in this paper. Fifth, a large literature on political economy considers the role of voting, lobbying, corruption, and political constitutions for the size of government. This literature has proposed that the democratization and increased political power of the poor have played an important role for the growth of government (Acemoglu and Robinson, 2000). Moreover, substantial attention has been paid to the relationship between changes in income distribution and voters demand for redistribution (Peltzman, 1980; Lindert, 2004). In addition to these hypotheses, a number of studies have pointed out that there are fiscal capacity constraints to government growth (e.g., Kau and Rubin, 1981; Bird, 1989, 1992; Peltzman, 1980; Riezman and Slemrod, 1987; Kenny and Winer, 2006; Aidt and Jensen, 2009). Moreover, there is a vast literature on the role of under-development in constraining tax structures both historically and in current developing countries. 9 Our theory proposes a micro-foundation that accounts for the changes in fiscal constraints over the course of development. Recently, Besley and Persson (2008, 2009) propose an extension of the ratchet e ect theory that emphasizes the role of increasing fiscal capacity over the course of development. They 9 See, e.g., Alt (1983), Bird and Oldman (1990), Gillis (1989), Hettich and Winer (1991), Hinrichs (1966), Kelley and Oldman (1973), Kenny and Winer (2006), Webber and Wildavsky (1996). 6

develop a model where governments invest in fiscal capacity over time in response to wars. Historically, major wars have often been associated with government investments in tax capacity such as information reporting and tax withholding. While wars have undoubtedly been instrumental in the increased fiscal capacity of some countries such as the United Kingdom, other countries such as Sweden have experienced a smooth growth in its tax-to-gdp ratio that appears unrelated to wars (we discuss the empirical evidence in more detail in section 4). Furthermore, the question remains why recent (20th century) wars have lead to large government expansions, whereas earlier wars typically have not. Our paper contributes to this question and is therefore complementary to the Besley-Persson theory. 3 A Micro Theory of Third-Party Tax Enforcement Let us assume that N individuals are working in a firm and receive pre-tax wages w = (w 1,.., w N ). The pre-tax profits of the firm are denoted by. Hence, the total value added created by the firm is equal to V = W + where W = P n w n are aggregate wages in the firm. Value added is also equal to total sales S minus purchases P. Let us assume that the government imposes a flat tax at rate on both wages and profits. If S and P are observable to the government, then value added V = W + = S P is also observable. As a result, under-reporting wages is useless to the firm because this would automatically increase its tax on profits. 10 However, if S and P are not observable to the government, then the firm can possibly under-report wages W without having to over-report profits. 11 In practice, S, P, and W (and hence ) would be observable to the government if the firm truthfully records this information in its business records (such as accounting books and payroll lists) and the government has access to these business records. Some firms may be able to carry out their business without recording this information formally. For example, a small family business might carry out all or part of its purchases and sales with cash and never record this information. On the other hand, maintaining accurate business records is clearly helpful to firm productivity: the business can measure its profits accurately, keep track of wages paid out, plan production activities, obtain access to financial sector services, formal insurance, etc. 10 If the tax rate on profits is lower than on wages, there is an incentive to under-report wages and over-report profits, and conversely. 11 For example, the firm could exaggerate purchases or underreport sales. Symmetrically, the firm could under-report profits without having to over-report wages. 7

Realistically, the productivity gain of keeping business records is larger when the firm is larger and more complex, and for modern firms the cost of being o -the-books becomes prohibitive. We therefore assume that the firm maintains accurate business records, which creates potentially detectable information within the firm. 12 However, even though business records exist, the firm may still be able to hide those records from the government to evade taxes. For example, the firm may maintain a double set of books, true books for business purposes and edited books for tax purposes. In this section, we present a simple agency theory showing how the government can truthfully extract the true business record information using third-party reporting. 13 Because we assume that the tax rate on profits and wages is the same, there are no incentives for profits and wage shifting and therefore wages and profits can be treated symmetrically. Hence, without loss of generality, we can model the owner of the profits as one additional wage earner, which simply amounts to ignoring profits (setting 0) in the analysis. 14 3.1 Agency Model with Third-Party Reporting 3.1.1 Basic Setup We assume that the government sets in place third-party reporting for tax purposes whereby each employee is required to report her earnings to the government and the firm is also required to report such individual earnings directly to the government. 15 Therefore, employees and employers have to agree on a wage report to the government as any discrepancy in the employer and employee reports would generate a tax audit. 16 We can therefore assume that the firm and employees agree on reports to the government given by w =( w 1,..., w N ), and this determines tax payments to the government unless any tax cheating is detected. We consider a situation where both real and reported wages (w, w) are determined cooperatively by the N employees of the firm. Because this is a tax collusion game, a 12 In Section 4.4, we consider the implications of endogenizing the choice of being on the books as in Gordon and Li (2005). 13 We focus primarily on third party reporting within the firm. We discuss briefly how third party reporting between firms, as happens with a value-added-tax, can also help enforcement. 14 To be sure, in practice, profits are di erent from wages because they are not recorded in the same way. Wages are recorded on payroll lists while profits are typically obtained by substraction as = S P W. 15 For example, in the United States, such reports are made through W2 forms issued by firms and sent to both the government and employees. Employees use this information to file their income tax returns (Logue and Slemrod, 2008 discuss this mechanism in detail). Some other OECD countries, such as Denmark, use prepopulated income tax returns whereby the government informs individuals about their earnings using information received from firms. 16 Indeed, tax agencies systematically search for discrepancies between employee and employer reports to target tax audits. 8

cooperative game seems to be the most natural one. 17 As solution concept, we consider the core: no coalition of employees can break o from the firm and obtain strictly better outcomes for each member of this splitting coalition. In particular, the outcome of the cooperative game is Pareto e cient (otherwise the coalition of all employees could do better) and therefore maximizes total surplus of the employees in the firm. In this section, we take N and the outside options of each employee as given. We denote by ȳ =(ȳ 1,..., ȳ N ) the disposable income levels (net of taxes) associated with those outside options. 18 Section 4, we fully endogenize outside options and firm size N. In the general equilibrium macro-model presented in The presence of business records creates common knowledge within the firm. We capture such common knowledge by assuming that (w, w) is known to everyone within the firm. In practice, although records may not be known to literally everyone within the firm, they are widely used in the firm and will be known by a number of employees. We explore also the alternative polar case where only employees for whom w n 6= w n are aware of tax evasion and can denounce tax cheating within the firm. This situation of private knowledge of tax evasion might be more realistic in the case of external parties such as business or individual clients, shareholders, or debt holders, a point we come back to later on. Following the report w to the government, taxes are paid at rate based on w. Each employee n =1,..., N then decides either to stick to the report w n or to whistleblow and reveal the true information to the government if w 6= w. We further assume that internal business records create verifiable information: If any employee whistleblows and reveals the information (w, w) of the company to the government and the government carries out an audit, the government will indeed be able to verify the information (w, w) with the cooperation of the whistleblower. Because true business records are widely used within the company, it is impossible to hide them if a single knowledgeable insider is determined to reveal the true information to the government. In contrast, if no employee is willing the break a collusive tax cheating agreement, then it is much harder for the government to discover the true information. For simplicity, in that case, we assume that the government cannot detect cheating at all. When evasion is detected, we assume that the government charges the evaded tax plus a 17 The substance of our results generalizes to a non-cooperative game. The non-cooperative case always makes tax enforcement easier relative to the cooperative case. 18 More precisely, we assume that outside options for any coalition of individuals is always given by ȳ = (ȳ 1,...,ȳ N ). 9

fine. As in all tax enforcement studies, we assume that there is an exogenous upper bound on the level of fines relative to tax evaded. 19 In that case, it is straightforward to show that it is always best for the government to impose the maximum possible fine in all circumstances. Therefore, without loss of generality, we assume that the penalty is equal to percent of the evaded tax to each person caught evading. In addition, the government may o er a reward to whistleblowers equal to a share all workers are risk neutral. 20 of total uncovered tax evasion. For simplicity, we assume that The timing of the game is as follows: (1) employees agree cooperatively on a vector of wages w =(w 1,..., w N ) and a vector of reports w =( w 1,..., w N ), (2) taxes are paid based on w at rate, (3) each employee n decides to stick to the report w n or to whistleblow if w 6= w, and (4) the government decides to audit or not, and fines and potential whistleblower rewards are paid. Proposition 1 If all employees can commit ex-ante never to denounce tax cheating to the government, then in any cooperative equilibrium in the core, we have w n =0for all n and no taxes are paid. Proof: Suppose that w n > 0 for some n. Then lowering w n to zero increases the distributable surplus by w n and hence can increase the payo of every employee without increasing the risk of detection as employees can commit not to denounce. Hence, (w, w) with P n w n > 0 cannot be in the core. QED. The complete cheating equilibrium result of Proposition 1 is unlikely to be robust in practice. There are two sets of reasons why employees may denounce tax cheating to the government. The first set of reasons is the presence of random shocks such as a conflict between an employee and the employer, moral concerns of a newly hired employee, or simply a mistake whereby an employee reveals the true records w to the government instead of the fake records w. second reason is the presence of rational whistleblowing if the government o ers a reward to whistleblowers. We develop both models below and show that, when firms are large, the result of Proposition 1 is not robust as tax evasion is bound to be uncovered, which deters it in the 19 Without such an upper bound, the government would impose infinite penalties and hence fully deter tax evasion in the first place. Such infinite fines are not tolerable in practice because punishment ought to be proportionate to the crime and because it is often very di cult to tell apart honest mistakes from intentional evasion. Therefore, imposing an upper bound on fines is both realistic and makes the tax enforcement theoretical problem non-trivial. 20 Assuming risk aversion would make tax enforcement easier for the government. We consider risk aversion in Section 3.2 in the context of the Allingham-Sandmo model. 10 The

first place. As we shall see, the random shock model shows that the evasion equilibrium is not robust to introducing a trembling hand, while the whistleblower model shows that the evasion equilibrium is not robust to relaxing the perfect commitment assumption. 3.1.2 Random Shock Model We incorporate the possibility that an employee may deviate and reveal internal business records either by mistake, because he is disgruntled, or because of moral concerns. 21 Let " be the probability of any given employee revealing true information through such random shocks. We assume for simplicity that those shocks are iid across employees. With N employees, nobody will denounce tax cheating with probability (1 ") N. The probability that somebody in the firm reveals true information (and hence triggers an audit) is therefore given by 1 (1 ") N. This probability is increasing in N, and tends to 1 as N tends to infinity as a random shock is bound to happen when the number of employees is very large. The expected pay-o of each employee equals y n = w n w n (1 (1 ") N ) (1 + ) (w n w n ) +. We assume that workers decide cooperatively on vectors of true and reported wages (w, w), taking as given the random shocks in the second stage. The possible outcomes of this cooperative game (the core) are characterized by the set of vectors (w, w) that maximize the total expected surplus Y = P n y n, subject to the resource constraint P N n=1 w n = W, non-negativity constraints w n, w n 0 for all n, and participation constraints y n ȳ n for all n, ensuring that each employee obtains a payo that is at least as high as his best available outside option ȳ n. The coalition of workers 1,..., N will find it optimal to increase or decrease the report w n for worker n depending on the derivative of total surplus with respect to w n. When w n <w n, we have: @Y @ w n = [ 1+(1+ )(1 (1 ") N )]. (1) When w n >w n, we have: @Y @ w n =, so that it never pays to over-report wages. 22 Proposition 2 In the random shock model, any cooperative solution is such that: 21 For example, an employee might no longer be able to condone tax cheating and decides to denounce the firm. Alternatively, a newly hired employee might not be willing to go along with tax cheating. 22 In principle, in case of over-reporting uncovered by an audit, overpaid taxes will be refunded. This would not change the fact that @Y/@ w n < 0 when w n >w n. 11

(a) If (1 ") N apple /(1 + ), there is no tax evasion at all: w = w. (b) If (1 ") N > /(1 + ), there is complete tax evasion: w =0. (c) For any > 0 and " > 0, there is N such as firms do not evade when N N. Proof: The proof of (a) and (b) is immediate as @Y/@ w n 0i (1 + )(1 (1 ") N ) 1 i /(1 + ) (1 ") N. For (b), where @Y/@ w n < 0, the solution is determined by the nonnegativity constraint w n 0 for all n. For (c), N is defined by /(1 + ) =(1 ") N, i.e., N = log( /(1 + ))/ log(1 "). QED. Four points are worth noting about Proposition 2. First, when " = 0, we are back to the standard collusive case where firm size does not help and there is always tax evasion. Second, when " > 0 and even for moderate fines > 0, it will always be the case that large firms choose not to evade, destroying the evasion equilibrium from Proposition 1. Our model can therefore explain why low fines and low audit rates can lead to successful enforcement in practice. This resolves the key puzzle of the Allingham-Sandmo model, which predicts extremely high evasion rates when audit rates and fines are low (given reasonable risk aversion parameters). Third, our qualitative results are robust to introducing risk aversion, which would make tax enforcement easier. Fourth, the results in the proposition do not depend on the specific division of revenue W across workers. The equilibrium division will depend on the outside opportunities ȳ and other factors not explicitly specified that determine the bargaining power of the individuals. Private vs. Common Knowledge of Cheating: The model above assumes that each employee has complete knowledge of the full set of wages w, w. An alternative polar assumption is that each worker knows only about his/her own wages w n, w n, while the employer is the only one knowing the full information (w, w). This private knowledge model is more realistic in the case of external parties such as business or individual clients, shareholders, or debt holders, which share specific information with the firm but might not know the complete information within the firm. Critically, we maintain the assumption that, if there is under-reporting for individual n ( w n <w n ) and individual n denounces the firm, the government will carry out an audit and then be able to observe the full set of actual and reported wages w, w. This assumption can be defended as follows. A formal business needs to record w and w. Individual n can prove that w n 6= w n as long as w n was formally paid out. Therefore, with hard evidence that the firm cheated on individual n, an investigation may 12

be able to retrieve the true business records and obtain full information w, w. In other words, the firm is a nexus of information written in the internal business records, and the information cannot be broken or hidden into isolated pieces. Proposition 3 In the random shock model with only private information on incomes: (a) The optimal evasion strategy for the firm is to report zero income for the N c highest-paid employees, where N c is an integer below N defined as [1 (1 ") N](1 + ) =1. (b) Assuming a fixed distribution of wage incomes, the fraction of income evaded tends to zero as N gets large. Proof: (a) If N c individuals evade, then the probability of detection equals 1 (1 ") Nc as only cheating individuals are able to denounce the firm. Hence, the total surplus is given by Y = X n [w n w n (1 (1 ") Nc ) (1 + ) (w n w n ) + ]. When w n <w n, we have: @Y @ w n = [ 1+(1+ )(1 (1 ") Nc )]. Therefore, evasion is profitable only if N c apple N defined as [1 (1 ") N](1 + ) = 1. An equilibrium with N c apple N evaders Pareto dominates an equilibrium with truthful reporting, because the payo from the N c evaders is higher due to underreporting, while the payo from everybody else is una ected. Moreover, when an employee evades, the surplus is maximized by full evasion: w n = 0. Because the extra surplus created by full evasion is proportional to w n, surplus is maximized by having the highest-paid employees evade. Given N c apple N, the optimal number of evaders reflects a trade-o between the extra surplus from the N c th evader and the higher probability of being caught for all other evaders. It is optimal to evade for at least one employee (the highest paid) i " (1 + ) apple 1, N 1. (b) Because N is fixed, as N goes to infinity, we have that N c /N apple N/N goes to zero a vanishing fraction of employees will be able to evade. If the wage distribution is fixed, the share of total compensation going to a vanishing fraction of employees also converges to zero. QED. Two points are worth noting about Proposition 3. First, our results of successful enforcement for large firms remains valid in the case of only private information, which is the least favorable 13

to tax enforcement. Second, this case may capture some of the real-world tax evasion practices of large firms. Most of the corporate income tax evasion does not take place as collusion to under-report the wages of ordinary employees, but takes place as under-reporting of profits by setting up illegal tax shelters. Such tax shelters are known or understood by a relatively small number of key accountants, a situation where the tax savings are large relative to the number of individuals in the know as in the proposition (see e.g., Slemrod 2004). Firms that plan on evading taxes therefore have an incentive to limit the flow of information within the firm. 3.1.3 Rational Whistleblower Model We now consider the case where the government o ers a whistleblower reward and we assume that each individual may voluntarily and rationally denounce their employer. Hence, we relax the critical assumption of ex-ante commitment from Proposition 1. In practice, firms do not have the power to enforce non-whistleblowing commitments. 23 We assume that the whistleblower reward is equal to a fraction of total uncovered revenue shared among all whistleblowers. 24 Several OECD countries use such whistleblower rewards to induce insiders to denounce large-scale tax evasion within firms. For example, in the United States, the IRS Whistleblower Reward Program o ers a payment of 15-30% of total uncovered tax revenue when whistleblowing leads to the detection of tax evasion in the excess of $2 million (Hesch, 2002). Related, Japan allows laid-o workers to claim unemployment benefits even if their employer did not pay social security contributions (OECD, 2004). evading social security taxes. 25 Such claims help the government discover businesses Alternatively, this model can be interpreted to capture moral rewards from denouncing large-scale tax cheating, assuming that each dollar of revenue that the whistleblower helps uncover creates a psychological reward of dollars. 26 Given payments w =(w 1,..., w N ) and reports w =( w 1,..., w N ), the payo for employee n if 23 Organized crime can succeed in enforcing non-whistleblowing agreements by threats of severe retaliation. Short of falling into organized crime, firms cannot impose severe retaliation (Dixit, 2004). In a dynamic model, it is conceivable that whistleblowers could be fired and hence lose future rents from the employment match. Such an extension would make enforcement harder, but would not change the essence of our results. 24 We discuss in Section 3.1.4 whether such a form of whistleblowing rewards can be seen as an optimal mechanism for the government to elicit tax compliance. 25 Interestingly, laid-o employees no longer derive surplus from the employment relationship and hence have less to lose when denouncing tax evasion than current employees. 26 If moral rewards are heterogeneous across individuals and unobservable by the employer, the model becomes conceptually very close to the random-shock model analyzed above. 14

he does not whistleblow is given by y n = w n w n a (1 + ) (w n w n ) +, (2) where a =0, 1 is an audit dummy that takes the value 1 if any employee whistleblows. The payo for employee n if he whistleblows (in which case a = 1) is given by y n = w n w n (1 + ) (w n w n ) + + (1 + ) P n (w 0 n 0 w n 0) +, (3) N w where N w denotes the number of whistleblowers who share equally the rewards from whistleblowing. We assume that the whistleblower reward is a share of total revenue (including fines), because this turns out to be notationally simpler below. From eqs (2)-(3), the total surplus in the firm can be written as Y = X wn 0 w n 0 a (1 )(1+ ) (w n 0 w n 0) +. (4) n 0 A cooperative solution (w, w) maximizes surplus Y subject to P n 0 w n 0 = W, non-negativity constraints w n, w n 0 for all n, and participation constraints y n ȳ n for all n. Notice that (1 )(1+ ) 1, apple / (1 + ) is required to avoid a situation where employees always evade and then collectively whistleblow in order to recoup larger rewards than the fines they pay for under-reporting in the first place. Moreover, because ex-ante commitments to not whistleblowing are infeasible, a cooperative solution with evasion must also satisfy incentive compatibility constraints ensuring that no worker finds it in his interest to whistleblow ex post. Therefore, given that co-workers do not whistleblow, utility for employee n must be higher under no whistleblowing (eq. 2 with a =0) than under whistleblowing (eq. 3 with N w = 1), implying that, for all n, apple (w n w n ) + Pn 0 (w n 0 w n 0) +. (5) On the other hand, if at least one co-worker whistleblows, employee n will always find it in his interest to also whistleblow. Proposition 4 In the whistleblower model, any cooperative solution is such that: (a) If N>1/, then there can be no tax evasion at all: w = w. Hence large firms do not evade taxes even if > 0 is very small. 15

(b) If N apple 1/, then some evasion is sustainable, and an outcome without evasion is Pareto dominated by a sustainable evasion equilibrium. In the evasion equilibrium, the lowest-paid employee always reports zero wages (full evasion). All other employees may report positive wages (less than full evasion), but evade by at least as much as the lowest-paid employee in absolute terms. If wages w 1,..., w N are equal, then all employees report zero wages. Proof: For (a), let us assume that N>1/ and that there is some evasion E P n (w 0 n 0 w n 0) > 0. Then, from eq. (5), we have w n w n E for all n. Summing across all n, this implies E N E. Because E>0, this implies 1 N, which is a contradiction. For (b), if some evasion is sustained (E >0), then we must have w n w n E for all n. Because apple 1 in this case, it is feasible to satisfy this condition, for example by having equal N evasion across all employees: w n w n = E E for all n. Thus, starting from an outcome N without evasion it is possible to reduce w n by a small amount d w for all n and thereby generate a sustainable Pareto improvement. The evasion equilibrium is characterized by the maximization of total surplus Y at a = 0 subject to P n w 0 n 0 = W, non-negativity w n, w n 0, participation constraints y n = w n w n ȳ n, and the no-whistleblowing constraint (5) for all n. In this case, total surplus is given by Y =(1 ) W + E, implying that the equilibrium maximizes E subject to w n w n E and w n 0, w n 0, w n w n ȳ n for all n. Because no employee can report negative wages, the no-whistleblowing constraint is hardest to satisfy for the lowest-paid individual, say employee 1, who can at the most evade by w 1 = min n w n ȳ n > 0. Therefore, to maximize E, there is full evasion for the lowest-paid employee ( w 1 = 0) and total evasion is taken to the point where (5) is binding for this employee, E = 1 w 1 Nw 1. All other employees evade by at least as much as the lowest-paid employee in absolute terms, w n w n w 1 for all n, but possibly by less in relative terms (less than full evasion). Obviously, if all wages are equal, then zero reporting by all employees is sustainable. QED. Three points are worth noting about Proposition 4. First, if = 0, i.e., if the government o ers no reward for whistleblowing, then all firms will evade taxes as in Proposition 1. Second, as soon as some reward > 0 is o ered, then tax evasion is no longer sustainable for large firms. Therefore, the whistleblowing model also shows that low-powered fines and audit rates are enough to sustain truthful reporting in large firms. This shows that the collusion equilibrium of Proposition 1 is not robust to relaxing the assumption of perfect commitment. Third, in this model, equality in the distribution of true wages w 1,..., w N has a positive impact on the 16

level of evasion that can be sustained in equilibrium. This is because low-paid workers are constrained in their evasion and therefore more tempted to whistleblow to get a share of total uncovered revenue. Because the wage structure is itself part of the cooperative evasion game, this creates an incentive for workers to agree on an equal wage structure so as to sustain full evasion. However, the equilibrium division of surplus depends also on the outside opportunities. In particular, complete wage equality and full tax evasion is not necessarily an equilibrium, because employees with good outside opportunities (presumably high-skilled workers) may not be willing to accept this division of surplus despite the extra tax evasion it delivers. Finally, we may also consider the case with only private knowledge about cheating. Let us assume that only employees involved in cheating can denounce the firm, and that they form rational expectations about the extent of total cheating within the firm. Consistent with the random shock model, we would again have that the firm o ers evasion to at most N c =1/ employees, and cheating will be concentrated among the highest-paid employees. As N becomes large, the fraction of employees evading and the share of total earnings evaded will shrink to zero. 3.1.4 Mechanism Design The general lesson from our model is that common information among tax payers dramatically increases the ability of the government to extract tax revenue even with bounded fines. We have proposed a whistleblowing mechanism, which achieves perfect enforcement when N is su ciently large. The natural question is whether this mechanism is globally optimal, or if the government could do even better. Three points are worth noting. First, when there is only one individual (N = 1) and keeping the assumption that the government can only successfully audit after whistleblowing, there is no mechanism that could induce the individual to reveal income truthfully. Second, if there is more than one individual (N 2), then in principle the government could design a non-conventional whistleblowing mechanism that induces truthful reporting. This mechanism is as follows: if the government receives information from N w whistleblowers, it will randomly select one whistleblower n, forgive n his evaded tax and corresponding fine, and o er n a small fraction of the tax evaded by the other individuals. 27 This mechanism would induce 27 This mechanism is non-conventional in the sense that we are not aware of any tax agency implementing it in practice. 17

any individual to denounce tax cheating and make tax collusion impossible to sustain as long as N 2. This strong implementation result is consistent with the mechanism design literature, which has shown that first best is often implementable in common information environments using su ciently sophisticated mechanisms (Moore, 1992). Third and most important, the complete enforcement result with a small number of individuals (N 2) is not robust. An insider is willing to whistleblow only if rewards from whistleblowing are larger than the loss of breaking the collusion agreement. In our 1-period model and under the non-conventional mechanism described above, there is no loss from breaking collusion. However, in practice, breaking a tax collusion may generate both monetary costs (loss of future surplus from the worker-firm match, search costs to find a new job, etc.) and psychological costs (in the form of a conflict with colleagues). If those costs are non-trivial, then the net rewards from whistleblowing need to be non-trivial as well, and in this case evasion can only be fully deterred when N is su ciently large. Therefore, we believe that the results we have presented capture the gist of the real-world tax policy problem. 3.1.5 The Role of External Business Records and the Scope of the Firm Our theory posits that the success of third-party reporting derives from the presence of verifiable internal business records that is commonly known among a su ciently large number of employees. It is useful to contrast our theory with situations where such records are not present, or when externally recorded transactions allow outside business partners to denounce the firm. External Business Records and Value-Added Taxes Information on income generated by a business can also be obtained from external transactions. For example, businesses need to provide accounting records to shareholders or debt providers. Value added (equal to the sum of wages and profits as we discussed above) can be inferred from value added taxes (all OECD countries except the United States impose value added taxes). The presence of publicly disclosed accounting books certainly imposes constraints on how much firms can evade as accounting books and corporate tax returns have to be consistent. Theoretically, the firm could collude with shareholders and banks to publicly disclose fake accounting books while secretly showing the true books to prospective shareholders and lenders. Exactly as in our model, such collusion would be very di cult to maintain with a large number of players. Therefore, firms which want to raise equity or debt need to maintain accurate 18